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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 20 Nov 2009 09:46:48 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/20/t1258735713hhfkch2dgo9ajb5.htm/, Retrieved Thu, 28 Mar 2024 17:06:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58322, Retrieved Thu, 28 Mar 2024 17:06:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Multi lineair reg...] [2009-11-19 19:35:22] [ba905ddf7cdf9ecb063c35348c4dab2e]
-   PD    [Multiple Regression] [multi ] [2009-11-20 16:46:48] [244731fa3e7e6c85774b8c0902c58f85] [Current]
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Dataseries X:
8.9	6.3
8.2	6.2
7.6	6.1
7.7	6.3
8.1	6.5
8.3	6.6
8.3	6.5
7.9	6.2
7.8	6.2
8	5.9
8.5	6.1
8.6	6.1
8.5	6.1
8	6.1
7.8	6.1
8	6.4
8.2	6.7
8.3	6.9
8.2	7
8.1	7
8	6.8
7.8	6.4
7.8	5.9
7.7	5.5
7.6	5.5
7.6	5.6
7.6	5.8
7.8	5.9
8	6.1
8	6.1
7.9	6
7.7	6
7.4	5.9
6.9	5.5
6.7	5.6
6.5	5.4
6.4	5.2
6.7	5.2
6.8	5.2
6.9	5.5
6.9	5.8
6.7	5.8
6.4	5.5
6.2	5.3
5.9	5.1
6.1	5.2
6.7	5.8
6.8	5.8
6.6	5.5
6.4	5
6.4	4.9
6.7	5.3
7.1	6.1
7.1	6.5
6.9	6.8
6.4	6.6
6	6.4
6	6.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
wm[t] = + 3.03276769585098 + 0.397803021818835wv[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
wm[t] =  +  3.03276769585098 +  0.397803021818835wv[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]wm[t] =  +  3.03276769585098 +  0.397803021818835wv[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
wm[t] = + 3.03276769585098 + 0.397803021818835wv[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.032767695850980.5375485.64191e-060
wv0.3978030218188350.0724245.49271e-061e-06

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 3.03276769585098 & 0.537548 & 5.6419 & 1e-06 & 0 \tabularnewline
wv & 0.397803021818835 & 0.072424 & 5.4927 & 1e-06 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]3.03276769585098[/C][C]0.537548[/C][C]5.6419[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]wv[/C][C]0.397803021818835[/C][C]0.072424[/C][C]5.4927[/C][C]1e-06[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.032767695850980.5375485.64191e-060
wv0.3978030218188350.0724245.49271e-061e-06







Multiple Linear Regression - Regression Statistics
Multiple R0.591710957513193
R-squared0.35012185724118
Adjusted R-squared0.338516890406201
F-TEST (value)30.1700006746995
F-TEST (DF numerator)1
F-TEST (DF denominator)56
p-value1.00029949146041e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.430961123434683
Sum Squared Residuals10.4007394350767

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.591710957513193 \tabularnewline
R-squared & 0.35012185724118 \tabularnewline
Adjusted R-squared & 0.338516890406201 \tabularnewline
F-TEST (value) & 30.1700006746995 \tabularnewline
F-TEST (DF numerator) & 1 \tabularnewline
F-TEST (DF denominator) & 56 \tabularnewline
p-value & 1.00029949146041e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.430961123434683 \tabularnewline
Sum Squared Residuals & 10.4007394350767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.591710957513193[/C][/ROW]
[ROW][C]R-squared[/C][C]0.35012185724118[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.338516890406201[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]30.1700006746995[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]1[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]56[/C][/ROW]
[ROW][C]p-value[/C][C]1.00029949146041e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.430961123434683[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]10.4007394350767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R0.591710957513193
R-squared0.35012185724118
Adjusted R-squared0.338516890406201
F-TEST (value)30.1700006746995
F-TEST (DF numerator)1
F-TEST (DF denominator)56
p-value1.00029949146041e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.430961123434683
Sum Squared Residuals10.4007394350767







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.36.57321459003865-0.273214590038652
26.26.29475247476543-0.0947524747654248
36.16.056070661674120.0439293383258764
46.36.095850963856010.204149036143993
56.56.254972172583540.245027827416459
66.66.334532776947310.265467223052692
76.56.334532776947310.165467223052692
86.26.175411568219770.0245884317802262
96.26.135631266037890.0643687339621099
105.96.21519187040166-0.315191870401657
116.16.41409338131107-0.314093381311075
126.16.45387368349296-0.353873683492958
136.16.41409338131107-0.314093381311075
146.16.21519187040166-0.115191870401658
156.16.13563126603789-0.0356312660378906
166.46.215191870401660.184808129598343
176.76.294752474765420.405247525234576
186.96.334532776947310.565467223052692
1976.294752474765420.705247525234576
2076.254972172583540.74502782741646
216.86.215191870401660.584808129598342
226.46.135631266037890.26436873396211
235.96.13563126603789-0.23563126603789
245.56.09585096385601-0.595850963856007
255.56.05607066167412-0.556070661674123
265.66.05607066167412-0.456070661674124
275.86.05607066167412-0.256070661674123
285.96.13563126603789-0.23563126603789
296.16.21519187040166-0.115191870401658
306.16.21519187040166-0.115191870401658
3166.17541156821977-0.175411568219774
3266.09585096385601-0.095850963856007
335.95.97651005731036-0.0765100573103562
345.55.77760854640094-0.277608546400939
355.65.69804794203717-0.0980479420371725
365.45.6184873376734-0.218487337673405
375.25.57870703549152-0.378707035491522
385.25.69804794203717-0.498047942037172
395.25.73782824421906-0.537828244219055
405.55.77760854640094-0.277608546400939
415.85.777608546400940.0223914535990607
425.85.698047942037170.101952057962828
435.55.57870703549152-0.0787070354915217
445.35.49914643112775-0.199146431127755
455.15.3798055245821-0.279805524582105
465.25.45936612894587-0.259366128945871
475.85.698047942037170.101952057962828
485.85.737828244219060.0621717557809444
495.55.65826763985529-0.158267639855288
5055.57870703549152-0.578707035491522
514.95.57870703549152-0.678707035491521
525.35.69804794203717-0.398047942037172
536.15.85716915076470.242830849235294
546.55.85716915076470.642830849235294
556.85.777608546400941.02239145359906
566.65.578707035491521.02129296450848
576.45.419585826763990.980414173236013
586.45.419585826763990.980414173236013

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 6.3 & 6.57321459003865 & -0.273214590038652 \tabularnewline
2 & 6.2 & 6.29475247476543 & -0.0947524747654248 \tabularnewline
3 & 6.1 & 6.05607066167412 & 0.0439293383258764 \tabularnewline
4 & 6.3 & 6.09585096385601 & 0.204149036143993 \tabularnewline
5 & 6.5 & 6.25497217258354 & 0.245027827416459 \tabularnewline
6 & 6.6 & 6.33453277694731 & 0.265467223052692 \tabularnewline
7 & 6.5 & 6.33453277694731 & 0.165467223052692 \tabularnewline
8 & 6.2 & 6.17541156821977 & 0.0245884317802262 \tabularnewline
9 & 6.2 & 6.13563126603789 & 0.0643687339621099 \tabularnewline
10 & 5.9 & 6.21519187040166 & -0.315191870401657 \tabularnewline
11 & 6.1 & 6.41409338131107 & -0.314093381311075 \tabularnewline
12 & 6.1 & 6.45387368349296 & -0.353873683492958 \tabularnewline
13 & 6.1 & 6.41409338131107 & -0.314093381311075 \tabularnewline
14 & 6.1 & 6.21519187040166 & -0.115191870401658 \tabularnewline
15 & 6.1 & 6.13563126603789 & -0.0356312660378906 \tabularnewline
16 & 6.4 & 6.21519187040166 & 0.184808129598343 \tabularnewline
17 & 6.7 & 6.29475247476542 & 0.405247525234576 \tabularnewline
18 & 6.9 & 6.33453277694731 & 0.565467223052692 \tabularnewline
19 & 7 & 6.29475247476542 & 0.705247525234576 \tabularnewline
20 & 7 & 6.25497217258354 & 0.74502782741646 \tabularnewline
21 & 6.8 & 6.21519187040166 & 0.584808129598342 \tabularnewline
22 & 6.4 & 6.13563126603789 & 0.26436873396211 \tabularnewline
23 & 5.9 & 6.13563126603789 & -0.23563126603789 \tabularnewline
24 & 5.5 & 6.09585096385601 & -0.595850963856007 \tabularnewline
25 & 5.5 & 6.05607066167412 & -0.556070661674123 \tabularnewline
26 & 5.6 & 6.05607066167412 & -0.456070661674124 \tabularnewline
27 & 5.8 & 6.05607066167412 & -0.256070661674123 \tabularnewline
28 & 5.9 & 6.13563126603789 & -0.23563126603789 \tabularnewline
29 & 6.1 & 6.21519187040166 & -0.115191870401658 \tabularnewline
30 & 6.1 & 6.21519187040166 & -0.115191870401658 \tabularnewline
31 & 6 & 6.17541156821977 & -0.175411568219774 \tabularnewline
32 & 6 & 6.09585096385601 & -0.095850963856007 \tabularnewline
33 & 5.9 & 5.97651005731036 & -0.0765100573103562 \tabularnewline
34 & 5.5 & 5.77760854640094 & -0.277608546400939 \tabularnewline
35 & 5.6 & 5.69804794203717 & -0.0980479420371725 \tabularnewline
36 & 5.4 & 5.6184873376734 & -0.218487337673405 \tabularnewline
37 & 5.2 & 5.57870703549152 & -0.378707035491522 \tabularnewline
38 & 5.2 & 5.69804794203717 & -0.498047942037172 \tabularnewline
39 & 5.2 & 5.73782824421906 & -0.537828244219055 \tabularnewline
40 & 5.5 & 5.77760854640094 & -0.277608546400939 \tabularnewline
41 & 5.8 & 5.77760854640094 & 0.0223914535990607 \tabularnewline
42 & 5.8 & 5.69804794203717 & 0.101952057962828 \tabularnewline
43 & 5.5 & 5.57870703549152 & -0.0787070354915217 \tabularnewline
44 & 5.3 & 5.49914643112775 & -0.199146431127755 \tabularnewline
45 & 5.1 & 5.3798055245821 & -0.279805524582105 \tabularnewline
46 & 5.2 & 5.45936612894587 & -0.259366128945871 \tabularnewline
47 & 5.8 & 5.69804794203717 & 0.101952057962828 \tabularnewline
48 & 5.8 & 5.73782824421906 & 0.0621717557809444 \tabularnewline
49 & 5.5 & 5.65826763985529 & -0.158267639855288 \tabularnewline
50 & 5 & 5.57870703549152 & -0.578707035491522 \tabularnewline
51 & 4.9 & 5.57870703549152 & -0.678707035491521 \tabularnewline
52 & 5.3 & 5.69804794203717 & -0.398047942037172 \tabularnewline
53 & 6.1 & 5.8571691507647 & 0.242830849235294 \tabularnewline
54 & 6.5 & 5.8571691507647 & 0.642830849235294 \tabularnewline
55 & 6.8 & 5.77760854640094 & 1.02239145359906 \tabularnewline
56 & 6.6 & 5.57870703549152 & 1.02129296450848 \tabularnewline
57 & 6.4 & 5.41958582676399 & 0.980414173236013 \tabularnewline
58 & 6.4 & 5.41958582676399 & 0.980414173236013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]6.3[/C][C]6.57321459003865[/C][C]-0.273214590038652[/C][/ROW]
[ROW][C]2[/C][C]6.2[/C][C]6.29475247476543[/C][C]-0.0947524747654248[/C][/ROW]
[ROW][C]3[/C][C]6.1[/C][C]6.05607066167412[/C][C]0.0439293383258764[/C][/ROW]
[ROW][C]4[/C][C]6.3[/C][C]6.09585096385601[/C][C]0.204149036143993[/C][/ROW]
[ROW][C]5[/C][C]6.5[/C][C]6.25497217258354[/C][C]0.245027827416459[/C][/ROW]
[ROW][C]6[/C][C]6.6[/C][C]6.33453277694731[/C][C]0.265467223052692[/C][/ROW]
[ROW][C]7[/C][C]6.5[/C][C]6.33453277694731[/C][C]0.165467223052692[/C][/ROW]
[ROW][C]8[/C][C]6.2[/C][C]6.17541156821977[/C][C]0.0245884317802262[/C][/ROW]
[ROW][C]9[/C][C]6.2[/C][C]6.13563126603789[/C][C]0.0643687339621099[/C][/ROW]
[ROW][C]10[/C][C]5.9[/C][C]6.21519187040166[/C][C]-0.315191870401657[/C][/ROW]
[ROW][C]11[/C][C]6.1[/C][C]6.41409338131107[/C][C]-0.314093381311075[/C][/ROW]
[ROW][C]12[/C][C]6.1[/C][C]6.45387368349296[/C][C]-0.353873683492958[/C][/ROW]
[ROW][C]13[/C][C]6.1[/C][C]6.41409338131107[/C][C]-0.314093381311075[/C][/ROW]
[ROW][C]14[/C][C]6.1[/C][C]6.21519187040166[/C][C]-0.115191870401658[/C][/ROW]
[ROW][C]15[/C][C]6.1[/C][C]6.13563126603789[/C][C]-0.0356312660378906[/C][/ROW]
[ROW][C]16[/C][C]6.4[/C][C]6.21519187040166[/C][C]0.184808129598343[/C][/ROW]
[ROW][C]17[/C][C]6.7[/C][C]6.29475247476542[/C][C]0.405247525234576[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.33453277694731[/C][C]0.565467223052692[/C][/ROW]
[ROW][C]19[/C][C]7[/C][C]6.29475247476542[/C][C]0.705247525234576[/C][/ROW]
[ROW][C]20[/C][C]7[/C][C]6.25497217258354[/C][C]0.74502782741646[/C][/ROW]
[ROW][C]21[/C][C]6.8[/C][C]6.21519187040166[/C][C]0.584808129598342[/C][/ROW]
[ROW][C]22[/C][C]6.4[/C][C]6.13563126603789[/C][C]0.26436873396211[/C][/ROW]
[ROW][C]23[/C][C]5.9[/C][C]6.13563126603789[/C][C]-0.23563126603789[/C][/ROW]
[ROW][C]24[/C][C]5.5[/C][C]6.09585096385601[/C][C]-0.595850963856007[/C][/ROW]
[ROW][C]25[/C][C]5.5[/C][C]6.05607066167412[/C][C]-0.556070661674123[/C][/ROW]
[ROW][C]26[/C][C]5.6[/C][C]6.05607066167412[/C][C]-0.456070661674124[/C][/ROW]
[ROW][C]27[/C][C]5.8[/C][C]6.05607066167412[/C][C]-0.256070661674123[/C][/ROW]
[ROW][C]28[/C][C]5.9[/C][C]6.13563126603789[/C][C]-0.23563126603789[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.21519187040166[/C][C]-0.115191870401658[/C][/ROW]
[ROW][C]30[/C][C]6.1[/C][C]6.21519187040166[/C][C]-0.115191870401658[/C][/ROW]
[ROW][C]31[/C][C]6[/C][C]6.17541156821977[/C][C]-0.175411568219774[/C][/ROW]
[ROW][C]32[/C][C]6[/C][C]6.09585096385601[/C][C]-0.095850963856007[/C][/ROW]
[ROW][C]33[/C][C]5.9[/C][C]5.97651005731036[/C][C]-0.0765100573103562[/C][/ROW]
[ROW][C]34[/C][C]5.5[/C][C]5.77760854640094[/C][C]-0.277608546400939[/C][/ROW]
[ROW][C]35[/C][C]5.6[/C][C]5.69804794203717[/C][C]-0.0980479420371725[/C][/ROW]
[ROW][C]36[/C][C]5.4[/C][C]5.6184873376734[/C][C]-0.218487337673405[/C][/ROW]
[ROW][C]37[/C][C]5.2[/C][C]5.57870703549152[/C][C]-0.378707035491522[/C][/ROW]
[ROW][C]38[/C][C]5.2[/C][C]5.69804794203717[/C][C]-0.498047942037172[/C][/ROW]
[ROW][C]39[/C][C]5.2[/C][C]5.73782824421906[/C][C]-0.537828244219055[/C][/ROW]
[ROW][C]40[/C][C]5.5[/C][C]5.77760854640094[/C][C]-0.277608546400939[/C][/ROW]
[ROW][C]41[/C][C]5.8[/C][C]5.77760854640094[/C][C]0.0223914535990607[/C][/ROW]
[ROW][C]42[/C][C]5.8[/C][C]5.69804794203717[/C][C]0.101952057962828[/C][/ROW]
[ROW][C]43[/C][C]5.5[/C][C]5.57870703549152[/C][C]-0.0787070354915217[/C][/ROW]
[ROW][C]44[/C][C]5.3[/C][C]5.49914643112775[/C][C]-0.199146431127755[/C][/ROW]
[ROW][C]45[/C][C]5.1[/C][C]5.3798055245821[/C][C]-0.279805524582105[/C][/ROW]
[ROW][C]46[/C][C]5.2[/C][C]5.45936612894587[/C][C]-0.259366128945871[/C][/ROW]
[ROW][C]47[/C][C]5.8[/C][C]5.69804794203717[/C][C]0.101952057962828[/C][/ROW]
[ROW][C]48[/C][C]5.8[/C][C]5.73782824421906[/C][C]0.0621717557809444[/C][/ROW]
[ROW][C]49[/C][C]5.5[/C][C]5.65826763985529[/C][C]-0.158267639855288[/C][/ROW]
[ROW][C]50[/C][C]5[/C][C]5.57870703549152[/C][C]-0.578707035491522[/C][/ROW]
[ROW][C]51[/C][C]4.9[/C][C]5.57870703549152[/C][C]-0.678707035491521[/C][/ROW]
[ROW][C]52[/C][C]5.3[/C][C]5.69804794203717[/C][C]-0.398047942037172[/C][/ROW]
[ROW][C]53[/C][C]6.1[/C][C]5.8571691507647[/C][C]0.242830849235294[/C][/ROW]
[ROW][C]54[/C][C]6.5[/C][C]5.8571691507647[/C][C]0.642830849235294[/C][/ROW]
[ROW][C]55[/C][C]6.8[/C][C]5.77760854640094[/C][C]1.02239145359906[/C][/ROW]
[ROW][C]56[/C][C]6.6[/C][C]5.57870703549152[/C][C]1.02129296450848[/C][/ROW]
[ROW][C]57[/C][C]6.4[/C][C]5.41958582676399[/C][C]0.980414173236013[/C][/ROW]
[ROW][C]58[/C][C]6.4[/C][C]5.41958582676399[/C][C]0.980414173236013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
16.36.57321459003865-0.273214590038652
26.26.29475247476543-0.0947524747654248
36.16.056070661674120.0439293383258764
46.36.095850963856010.204149036143993
56.56.254972172583540.245027827416459
66.66.334532776947310.265467223052692
76.56.334532776947310.165467223052692
86.26.175411568219770.0245884317802262
96.26.135631266037890.0643687339621099
105.96.21519187040166-0.315191870401657
116.16.41409338131107-0.314093381311075
126.16.45387368349296-0.353873683492958
136.16.41409338131107-0.314093381311075
146.16.21519187040166-0.115191870401658
156.16.13563126603789-0.0356312660378906
166.46.215191870401660.184808129598343
176.76.294752474765420.405247525234576
186.96.334532776947310.565467223052692
1976.294752474765420.705247525234576
2076.254972172583540.74502782741646
216.86.215191870401660.584808129598342
226.46.135631266037890.26436873396211
235.96.13563126603789-0.23563126603789
245.56.09585096385601-0.595850963856007
255.56.05607066167412-0.556070661674123
265.66.05607066167412-0.456070661674124
275.86.05607066167412-0.256070661674123
285.96.13563126603789-0.23563126603789
296.16.21519187040166-0.115191870401658
306.16.21519187040166-0.115191870401658
3166.17541156821977-0.175411568219774
3266.09585096385601-0.095850963856007
335.95.97651005731036-0.0765100573103562
345.55.77760854640094-0.277608546400939
355.65.69804794203717-0.0980479420371725
365.45.6184873376734-0.218487337673405
375.25.57870703549152-0.378707035491522
385.25.69804794203717-0.498047942037172
395.25.73782824421906-0.537828244219055
405.55.77760854640094-0.277608546400939
415.85.777608546400940.0223914535990607
425.85.698047942037170.101952057962828
435.55.57870703549152-0.0787070354915217
445.35.49914643112775-0.199146431127755
455.15.3798055245821-0.279805524582105
465.25.45936612894587-0.259366128945871
475.85.698047942037170.101952057962828
485.85.737828244219060.0621717557809444
495.55.65826763985529-0.158267639855288
5055.57870703549152-0.578707035491522
514.95.57870703549152-0.678707035491521
525.35.69804794203717-0.398047942037172
536.15.85716915076470.242830849235294
546.55.85716915076470.642830849235294
556.85.777608546400941.02239145359906
566.65.578707035491521.02129296450848
576.45.419585826763990.980414173236013
586.45.419585826763990.980414173236013







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.06051379861503240.1210275972300650.939486201384968
60.05774008120903420.1154801624180680.942259918790966
70.02643042040170750.05286084080341510.973569579598292
80.01090750276241240.02181500552482490.989092497237588
90.003961708491997750.00792341698399550.996038291508002
100.009416427187872810.01883285437574560.990583572812127
110.006985191593469920.01397038318693980.99301480840653
120.004558697559600830.009117395119201660.9954413024404
130.002572035561989260.005144071123978510.99742796443801
140.001211281120402570.002422562240805140.998788718879597
150.0005191110054731030.001038222010946210.999480888994527
160.0002857922328647830.0005715844657295660.999714207767135
170.0008104415155942770.001620883031188550.999189558484406
180.004539140789806420.009078281579612840.995460859210194
190.02147048362738140.04294096725476290.978529516372619
200.06312464297523480.1262492859504700.936875357024765
210.0875149907676260.1750299815352520.912485009232374
220.068057378676380.136114757352760.93194262132362
230.0662269527380820.1324539054761640.933773047261918
240.1269566886834350.253913377366870.873043311316565
250.1673206881485150.3346413762970310.832679311851485
260.1671480555869690.3342961111739380.832851944413031
270.1316632953635100.2633265907270200.86833670463649
280.1006881421829380.2013762843658760.899311857817062
290.07148464440012480.1429692888002500.928515355599875
300.04923785043884210.09847570087768430.950762149561158
310.03359098987732400.06718197975464790.966409010122676
320.02140665286791480.04281330573582960.978593347132085
330.01317131712364950.0263426342472990.98682868287635
340.00858382398560910.01716764797121820.99141617601439
350.005169699792959250.01033939958591850.99483030020704
360.003106032935105510.006212065870211030.996893967064894
370.002191334794204710.004382669588409420.997808665205795
380.0020462429834190.0040924859668380.99795375701658
390.002293452740069210.004586905480138410.99770654725993
400.001603625173638080.003207250347276160.998396374826362
410.0009928642059333960.001985728411866790.999007135794067
420.0006495575413501130.001299115082700230.99935044245865
430.0003673840385958380.0007347680771916760.999632615961404
440.0002121807660651210.0004243615321302410.999787819233935
450.0001473160291217200.0002946320582434400.999852683970878
460.0001271041683408750.0002542083366817510.99987289583166
476.66496981859274e-050.0001332993963718550.999933350301814
483.12618384571333e-056.25236769142666e-050.999968738161543
491.97475682157916e-053.94951364315832e-050.999980252431784
500.0001617914367755010.0003235828735510020.999838208563224
510.01846901282507000.03693802565014010.98153098717493
520.5730639034688840.8538721930622320.426936096531116
530.8690642506884480.2618714986231050.130935749311552

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
5 & 0.0605137986150324 & 0.121027597230065 & 0.939486201384968 \tabularnewline
6 & 0.0577400812090342 & 0.115480162418068 & 0.942259918790966 \tabularnewline
7 & 0.0264304204017075 & 0.0528608408034151 & 0.973569579598292 \tabularnewline
8 & 0.0109075027624124 & 0.0218150055248249 & 0.989092497237588 \tabularnewline
9 & 0.00396170849199775 & 0.0079234169839955 & 0.996038291508002 \tabularnewline
10 & 0.00941642718787281 & 0.0188328543757456 & 0.990583572812127 \tabularnewline
11 & 0.00698519159346992 & 0.0139703831869398 & 0.99301480840653 \tabularnewline
12 & 0.00455869755960083 & 0.00911739511920166 & 0.9954413024404 \tabularnewline
13 & 0.00257203556198926 & 0.00514407112397851 & 0.99742796443801 \tabularnewline
14 & 0.00121128112040257 & 0.00242256224080514 & 0.998788718879597 \tabularnewline
15 & 0.000519111005473103 & 0.00103822201094621 & 0.999480888994527 \tabularnewline
16 & 0.000285792232864783 & 0.000571584465729566 & 0.999714207767135 \tabularnewline
17 & 0.000810441515594277 & 0.00162088303118855 & 0.999189558484406 \tabularnewline
18 & 0.00453914078980642 & 0.00907828157961284 & 0.995460859210194 \tabularnewline
19 & 0.0214704836273814 & 0.0429409672547629 & 0.978529516372619 \tabularnewline
20 & 0.0631246429752348 & 0.126249285950470 & 0.936875357024765 \tabularnewline
21 & 0.087514990767626 & 0.175029981535252 & 0.912485009232374 \tabularnewline
22 & 0.06805737867638 & 0.13611475735276 & 0.93194262132362 \tabularnewline
23 & 0.066226952738082 & 0.132453905476164 & 0.933773047261918 \tabularnewline
24 & 0.126956688683435 & 0.25391337736687 & 0.873043311316565 \tabularnewline
25 & 0.167320688148515 & 0.334641376297031 & 0.832679311851485 \tabularnewline
26 & 0.167148055586969 & 0.334296111173938 & 0.832851944413031 \tabularnewline
27 & 0.131663295363510 & 0.263326590727020 & 0.86833670463649 \tabularnewline
28 & 0.100688142182938 & 0.201376284365876 & 0.899311857817062 \tabularnewline
29 & 0.0714846444001248 & 0.142969288800250 & 0.928515355599875 \tabularnewline
30 & 0.0492378504388421 & 0.0984757008776843 & 0.950762149561158 \tabularnewline
31 & 0.0335909898773240 & 0.0671819797546479 & 0.966409010122676 \tabularnewline
32 & 0.0214066528679148 & 0.0428133057358296 & 0.978593347132085 \tabularnewline
33 & 0.0131713171236495 & 0.026342634247299 & 0.98682868287635 \tabularnewline
34 & 0.0085838239856091 & 0.0171676479712182 & 0.99141617601439 \tabularnewline
35 & 0.00516969979295925 & 0.0103393995859185 & 0.99483030020704 \tabularnewline
36 & 0.00310603293510551 & 0.00621206587021103 & 0.996893967064894 \tabularnewline
37 & 0.00219133479420471 & 0.00438266958840942 & 0.997808665205795 \tabularnewline
38 & 0.002046242983419 & 0.004092485966838 & 0.99795375701658 \tabularnewline
39 & 0.00229345274006921 & 0.00458690548013841 & 0.99770654725993 \tabularnewline
40 & 0.00160362517363808 & 0.00320725034727616 & 0.998396374826362 \tabularnewline
41 & 0.000992864205933396 & 0.00198572841186679 & 0.999007135794067 \tabularnewline
42 & 0.000649557541350113 & 0.00129911508270023 & 0.99935044245865 \tabularnewline
43 & 0.000367384038595838 & 0.000734768077191676 & 0.999632615961404 \tabularnewline
44 & 0.000212180766065121 & 0.000424361532130241 & 0.999787819233935 \tabularnewline
45 & 0.000147316029121720 & 0.000294632058243440 & 0.999852683970878 \tabularnewline
46 & 0.000127104168340875 & 0.000254208336681751 & 0.99987289583166 \tabularnewline
47 & 6.66496981859274e-05 & 0.000133299396371855 & 0.999933350301814 \tabularnewline
48 & 3.12618384571333e-05 & 6.25236769142666e-05 & 0.999968738161543 \tabularnewline
49 & 1.97475682157916e-05 & 3.94951364315832e-05 & 0.999980252431784 \tabularnewline
50 & 0.000161791436775501 & 0.000323582873551002 & 0.999838208563224 \tabularnewline
51 & 0.0184690128250700 & 0.0369380256501401 & 0.98153098717493 \tabularnewline
52 & 0.573063903468884 & 0.853872193062232 & 0.426936096531116 \tabularnewline
53 & 0.869064250688448 & 0.261871498623105 & 0.130935749311552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]5[/C][C]0.0605137986150324[/C][C]0.121027597230065[/C][C]0.939486201384968[/C][/ROW]
[ROW][C]6[/C][C]0.0577400812090342[/C][C]0.115480162418068[/C][C]0.942259918790966[/C][/ROW]
[ROW][C]7[/C][C]0.0264304204017075[/C][C]0.0528608408034151[/C][C]0.973569579598292[/C][/ROW]
[ROW][C]8[/C][C]0.0109075027624124[/C][C]0.0218150055248249[/C][C]0.989092497237588[/C][/ROW]
[ROW][C]9[/C][C]0.00396170849199775[/C][C]0.0079234169839955[/C][C]0.996038291508002[/C][/ROW]
[ROW][C]10[/C][C]0.00941642718787281[/C][C]0.0188328543757456[/C][C]0.990583572812127[/C][/ROW]
[ROW][C]11[/C][C]0.00698519159346992[/C][C]0.0139703831869398[/C][C]0.99301480840653[/C][/ROW]
[ROW][C]12[/C][C]0.00455869755960083[/C][C]0.00911739511920166[/C][C]0.9954413024404[/C][/ROW]
[ROW][C]13[/C][C]0.00257203556198926[/C][C]0.00514407112397851[/C][C]0.99742796443801[/C][/ROW]
[ROW][C]14[/C][C]0.00121128112040257[/C][C]0.00242256224080514[/C][C]0.998788718879597[/C][/ROW]
[ROW][C]15[/C][C]0.000519111005473103[/C][C]0.00103822201094621[/C][C]0.999480888994527[/C][/ROW]
[ROW][C]16[/C][C]0.000285792232864783[/C][C]0.000571584465729566[/C][C]0.999714207767135[/C][/ROW]
[ROW][C]17[/C][C]0.000810441515594277[/C][C]0.00162088303118855[/C][C]0.999189558484406[/C][/ROW]
[ROW][C]18[/C][C]0.00453914078980642[/C][C]0.00907828157961284[/C][C]0.995460859210194[/C][/ROW]
[ROW][C]19[/C][C]0.0214704836273814[/C][C]0.0429409672547629[/C][C]0.978529516372619[/C][/ROW]
[ROW][C]20[/C][C]0.0631246429752348[/C][C]0.126249285950470[/C][C]0.936875357024765[/C][/ROW]
[ROW][C]21[/C][C]0.087514990767626[/C][C]0.175029981535252[/C][C]0.912485009232374[/C][/ROW]
[ROW][C]22[/C][C]0.06805737867638[/C][C]0.13611475735276[/C][C]0.93194262132362[/C][/ROW]
[ROW][C]23[/C][C]0.066226952738082[/C][C]0.132453905476164[/C][C]0.933773047261918[/C][/ROW]
[ROW][C]24[/C][C]0.126956688683435[/C][C]0.25391337736687[/C][C]0.873043311316565[/C][/ROW]
[ROW][C]25[/C][C]0.167320688148515[/C][C]0.334641376297031[/C][C]0.832679311851485[/C][/ROW]
[ROW][C]26[/C][C]0.167148055586969[/C][C]0.334296111173938[/C][C]0.832851944413031[/C][/ROW]
[ROW][C]27[/C][C]0.131663295363510[/C][C]0.263326590727020[/C][C]0.86833670463649[/C][/ROW]
[ROW][C]28[/C][C]0.100688142182938[/C][C]0.201376284365876[/C][C]0.899311857817062[/C][/ROW]
[ROW][C]29[/C][C]0.0714846444001248[/C][C]0.142969288800250[/C][C]0.928515355599875[/C][/ROW]
[ROW][C]30[/C][C]0.0492378504388421[/C][C]0.0984757008776843[/C][C]0.950762149561158[/C][/ROW]
[ROW][C]31[/C][C]0.0335909898773240[/C][C]0.0671819797546479[/C][C]0.966409010122676[/C][/ROW]
[ROW][C]32[/C][C]0.0214066528679148[/C][C]0.0428133057358296[/C][C]0.978593347132085[/C][/ROW]
[ROW][C]33[/C][C]0.0131713171236495[/C][C]0.026342634247299[/C][C]0.98682868287635[/C][/ROW]
[ROW][C]34[/C][C]0.0085838239856091[/C][C]0.0171676479712182[/C][C]0.99141617601439[/C][/ROW]
[ROW][C]35[/C][C]0.00516969979295925[/C][C]0.0103393995859185[/C][C]0.99483030020704[/C][/ROW]
[ROW][C]36[/C][C]0.00310603293510551[/C][C]0.00621206587021103[/C][C]0.996893967064894[/C][/ROW]
[ROW][C]37[/C][C]0.00219133479420471[/C][C]0.00438266958840942[/C][C]0.997808665205795[/C][/ROW]
[ROW][C]38[/C][C]0.002046242983419[/C][C]0.004092485966838[/C][C]0.99795375701658[/C][/ROW]
[ROW][C]39[/C][C]0.00229345274006921[/C][C]0.00458690548013841[/C][C]0.99770654725993[/C][/ROW]
[ROW][C]40[/C][C]0.00160362517363808[/C][C]0.00320725034727616[/C][C]0.998396374826362[/C][/ROW]
[ROW][C]41[/C][C]0.000992864205933396[/C][C]0.00198572841186679[/C][C]0.999007135794067[/C][/ROW]
[ROW][C]42[/C][C]0.000649557541350113[/C][C]0.00129911508270023[/C][C]0.99935044245865[/C][/ROW]
[ROW][C]43[/C][C]0.000367384038595838[/C][C]0.000734768077191676[/C][C]0.999632615961404[/C][/ROW]
[ROW][C]44[/C][C]0.000212180766065121[/C][C]0.000424361532130241[/C][C]0.999787819233935[/C][/ROW]
[ROW][C]45[/C][C]0.000147316029121720[/C][C]0.000294632058243440[/C][C]0.999852683970878[/C][/ROW]
[ROW][C]46[/C][C]0.000127104168340875[/C][C]0.000254208336681751[/C][C]0.99987289583166[/C][/ROW]
[ROW][C]47[/C][C]6.66496981859274e-05[/C][C]0.000133299396371855[/C][C]0.999933350301814[/C][/ROW]
[ROW][C]48[/C][C]3.12618384571333e-05[/C][C]6.25236769142666e-05[/C][C]0.999968738161543[/C][/ROW]
[ROW][C]49[/C][C]1.97475682157916e-05[/C][C]3.94951364315832e-05[/C][C]0.999980252431784[/C][/ROW]
[ROW][C]50[/C][C]0.000161791436775501[/C][C]0.000323582873551002[/C][C]0.999838208563224[/C][/ROW]
[ROW][C]51[/C][C]0.0184690128250700[/C][C]0.0369380256501401[/C][C]0.98153098717493[/C][/ROW]
[ROW][C]52[/C][C]0.573063903468884[/C][C]0.853872193062232[/C][C]0.426936096531116[/C][/ROW]
[ROW][C]53[/C][C]0.869064250688448[/C][C]0.261871498623105[/C][C]0.130935749311552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=5

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
50.06051379861503240.1210275972300650.939486201384968
60.05774008120903420.1154801624180680.942259918790966
70.02643042040170750.05286084080341510.973569579598292
80.01090750276241240.02181500552482490.989092497237588
90.003961708491997750.00792341698399550.996038291508002
100.009416427187872810.01883285437574560.990583572812127
110.006985191593469920.01397038318693980.99301480840653
120.004558697559600830.009117395119201660.9954413024404
130.002572035561989260.005144071123978510.99742796443801
140.001211281120402570.002422562240805140.998788718879597
150.0005191110054731030.001038222010946210.999480888994527
160.0002857922328647830.0005715844657295660.999714207767135
170.0008104415155942770.001620883031188550.999189558484406
180.004539140789806420.009078281579612840.995460859210194
190.02147048362738140.04294096725476290.978529516372619
200.06312464297523480.1262492859504700.936875357024765
210.0875149907676260.1750299815352520.912485009232374
220.068057378676380.136114757352760.93194262132362
230.0662269527380820.1324539054761640.933773047261918
240.1269566886834350.253913377366870.873043311316565
250.1673206881485150.3346413762970310.832679311851485
260.1671480555869690.3342961111739380.832851944413031
270.1316632953635100.2633265907270200.86833670463649
280.1006881421829380.2013762843658760.899311857817062
290.07148464440012480.1429692888002500.928515355599875
300.04923785043884210.09847570087768430.950762149561158
310.03359098987732400.06718197975464790.966409010122676
320.02140665286791480.04281330573582960.978593347132085
330.01317131712364950.0263426342472990.98682868287635
340.00858382398560910.01716764797121820.99141617601439
350.005169699792959250.01033939958591850.99483030020704
360.003106032935105510.006212065870211030.996893967064894
370.002191334794204710.004382669588409420.997808665205795
380.0020462429834190.0040924859668380.99795375701658
390.002293452740069210.004586905480138410.99770654725993
400.001603625173638080.003207250347276160.998396374826362
410.0009928642059333960.001985728411866790.999007135794067
420.0006495575413501130.001299115082700230.99935044245865
430.0003673840385958380.0007347680771916760.999632615961404
440.0002121807660651210.0004243615321302410.999787819233935
450.0001473160291217200.0002946320582434400.999852683970878
460.0001271041683408750.0002542083366817510.99987289583166
476.66496981859274e-050.0001332993963718550.999933350301814
483.12618384571333e-056.25236769142666e-050.999968738161543
491.97475682157916e-053.94951364315832e-050.999980252431784
500.0001617914367755010.0003235828735510020.999838208563224
510.01846901282507000.03693802565014010.98153098717493
520.5730639034688840.8538721930622320.426936096531116
530.8690642506884480.2618714986231050.130935749311552







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level230.469387755102041NOK
5% type I error level320.653061224489796NOK
10% type I error level350.714285714285714NOK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 23 & 0.469387755102041 & NOK \tabularnewline
5% type I error level & 32 & 0.653061224489796 & NOK \tabularnewline
10% type I error level & 35 & 0.714285714285714 & NOK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58322&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]23[/C][C]0.469387755102041[/C][C]NOK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]32[/C][C]0.653061224489796[/C][C]NOK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]35[/C][C]0.714285714285714[/C][C]NOK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58322&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58322&T=6

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level230.469387755102041NOK
5% type I error level320.653061224489796NOK
10% type I error level350.714285714285714NOK



Parameters (Session):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}